scholarly journals On Cauchy problems for fuzzy differential equations

2004 ◽  
Vol 2004 (15) ◽  
pp. 799-805 ◽  
Author(s):  
D. N. Georgiou ◽  
I. E. Kougias
Keyword(s):  
Differential Equations ◽  
Existence And Uniqueness ◽  
Second Order ◽  
Uniqueness Theorems ◽  
Cauchy Problems ◽  
Existence And Uniqueness Theorems

Existence and uniqueness theorems are proved for Cauchy problems of second-order fuzzy differential equations.

scholarly journals A reinterpretation of set differential equations as differential equations in a Banach space

2017 ◽  
Vol 148 (2) ◽  
pp. 429-446
Author(s):  
Martin Rasmussen ◽  
Janosch Rieger ◽  
Kevin Webster
Keyword(s):  
Banach Space ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Existence And Uniqueness ◽  
Geometric Interpretation ◽  
Uniqueness Theorems ◽  
Support Functions ◽  
Existence And Uniqueness Theorems ◽  
Compact Subsets

Set differential equations are usually formulated in terms of the Hukuhara differential. As a consequence, the theory of set differential equations is perceived as an independent subject, in which all results are proved within the framework of the Hukuhara calculus. We propose to reformulate set differential equations as ordinary differential equations in a Banach space by identifying the convex and compact subsets of ℝd with their support functions. Using this representation, standard existence and uniqueness theorems for ordinary differential equations can be applied to set differential equations. We provide a geometric interpretation of the main result, and demonstrate that our approach overcomes the heavy restrictions that the use of the Hukuhara differential implies for the nature of a solution.

scholarly journals The existence and uniqueness theorems of fuzzy delay differential equations

2014 ◽  
Vol 10 (3) ◽  
Author(s):  
Nor Atirah Izzah Zulkefli ◽  
Normah Maan
Keyword(s):  
Dynamical System ◽  
Differential Equations ◽  
Delay Differential Equations ◽  
Existence And Uniqueness ◽  
Realistic Model ◽  
Uniqueness Theorems ◽  
Existence And Uniqueness Theorems ◽  
New Directions ◽  
Delay Differential ◽  
Real World Problems

Delay differential equations (DDEs) arise many different phenomena including in physics, biology and chemistry. In many cases of the modeling of real world problems, information about the behaviour of a dynamical system is uncertain. In order to obtain a more realistic model, we have to take into account these uncertainties. Therefore, in this paper, we propose the existence and uniqueness theorems for fuzzy time-delay dynamical systems. We finally present some conclusions and new directions for further research in this area.

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